why does log a + log b = log (ab)

Let log a be some number A and log b be some number B

now the natural log of something is the equivalent of saying a=e^A and b = e^B

So a*b = e^A * e^B which by rules of indices

 = e^(A+B)

Therefore log(ab) = log(e^(A+B))

= A + B = log a + log b 

RV
Answered by Rebecca V. Maths tutor

4579 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integral of (cos(x))^2 or (sin(x))^2


Simplify (7+sqrt(5))/(sqrt(5)-1), leaving the answer in the form a+b*sqrt(5)


(a) By using a suitable trigonometrical identity, solve the equation tan(2x-π/6)^2 =11-sec(2x-π/6)giving all values of x in radians to two decimal places in the interval 0<=x <=π .


Find the derivative of sin(x)/x^3 with respect to x


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences